Math 151 , Day 5 Monday, Sept. 9, Fall 2002 Hit
reload to get most current version..REVISED
+Next time (Wednesday) meet in Mac 101.
Bring Text, a floppy or Zipdisk.
+Friday I will not be here, but the Mac 101 lab
will be open for you, and there will be SPSS work to do. I strongly
suggest coming together in the lab at class time and working together on
the SPSS.
+ math151@wells.edu
, our class email list, has been formed, using our Wells mail addresses.
You can easily access your
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address http://webmail.wells.edu.
In there you can
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+Handout for Density curve homework (sec.
1.3)
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HW Day 5, Monday, Sept. 9
PLEASE read ahead in 1.3, Normal Distributions:
There's a lot there, and I will cover a good chunk Monday
Do After reading pp.37-40,standard deviation:
Hand in (combined with the parts done last time.)
p.
40, 1.34 a, b. Graph the data with a dotplot. Use SPSS to do
c.
1.35 (Maris HR-w/w.o.outliers)Don't forget
the dotplot! Use SPSS for calculations.
p. 44, 1.42 xbar=7.50, s = 2.03, the same
for both dist's--compare their shapes! |
Read, to discuss
1.43 states' oldies: which?why? (don't calculate)
|
Optional |
Do After reading sec. 1.3, pp. 46-51:
Hand in next Wednesday
Density homework HANDOUT, do both sides.
p. 51, 1.50, 51, 52 general densities, mean
&median |
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(ACTIVSTATS 6-1&2( boxplots). 4.2 (s.d). 5-1 (Densities), Ahead 3-4
(Shape, inc. Normal Distribution ) 5.2&3 Normal.
SPSS activities are throughout the lessons--you can find them specifically
by looking up SPSS in the index.)
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HW questions?
Review five number summary, boxplot, IQR Day
4
SPSS, for simple computation: Handout
Standard deviation (goes with mean)
Variance s2: (almost) average
of squared deviations from the mean.
(Divide by (n-1)
"degrees of freedom")
s : Standard deviation is the square
root of the variance.
Computation: I will require you to know how to do it by hand for
4 or 5 observations(see p. 39 for pattern).
Physics: angular momemtum (spinning ice skater)
Not so weird: High school geometry?
Remember Pythagorean theorem: c2
=
a2 + b2:
hypotenuse of right triangle is also square root of a sum of squares.
Very
sensitive to outliers (squared deviations do it)
Mean/standard deviation
pair useful for symmetric, unimodal (one-humped), no outliers. ("Normal"
dist.)
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Density curves, pp.46-51
(When values can take on any of a continuous interval
of numbers)
Example: Spinner: Label edge with continuous values from
0 to 1. Spinning should produce 1/10 of all spins in each colored sector.
Simulations of 500, 3000 spins show roughly true. More spins would get
closer.
Abstraction, idealized histogram ("Mathematical model") = Density
curve. Theoretical distribution of data.
Any density curve: is a curve
--always on or above the horizontal axis
--has area exactly 1 underneath it.
This allows area to represent proportion of "histogram" between
specified values.
(Continuing here Monday)
(We will assume the proportion
of observations precisely
equal to a value is 0. "So proportion
less than 2" is the same number as "proportion less than or equal to 2.")
Many, many density curves are possible, modeling
many phenomena.
For the spinner, the density curve is "Uniform on
0 to 1".
Take two spinners like this, spin both at once and
add the results--the corresponding density curve is "triangular, symmetric,
on 0 to 2"
A more complicated mechanism will produce data corresponding
to the density curve I have called "trapezoid, -1 to 2"
A very important one is the "normal" distribution
family.
Median, mean, percentiles, standard deviation
are defined for a density curve in analogy to those for a histogram.
-- median has half of area below
and half above.
-- mean is balance point. On the
long-tail side of median if distribution is skewed. Same as median if symmetric.
--First quartile has 1/4 of area below,
3/4 above. Etc. for others.
Tables are used to describe many densities.
Especially tables showing area to the left of (below) a given value.
Or to the right of (above) a given value.
You will make and use tables for the simple distributions
on the handout. These are similar to the table we will use to describe
the normal distribution.
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